We present the measurements of the energy spectra of carbon and oxygen nuclei in cosmic rays based on 4 years of observation with the Calorimetric Electron Telescope (CALET) on the International Space Station. The energy spectra are measured from 10 GeV/n to 2.2 TeV/n with an all calorimetric instrument with a total thickness corresponding to 1.3 nuclear interaction length and equipped with charge detectors capable of single element resolution. Data analysis, including the detailed assessment of systematic uncertainties, and results are reported. The observed carbon and oxygen fluxes show a spectral hardening around 200 GeV/n established with a significance > 3σ. They have the same energy dependence and a constant C/O flux ratio above 25 GeV/n. These measurements will contribute to a better understanding of the origin of the spectral hardening.